Fourierov integral

begin

    using PortAudio, SampledSignals

    import LibSndFile

    using FileIO: load, save, loadstreaming, savestreaming, query

    # using QuadGK

end

# pkg> add https://github.com/JuliaAudio/PortAudio.jl.git

PortAudio.devices()

#=

stream = PortAudioStream(2, 2)

try

    # cancel with Ctrl-C

    write(stream, stream)

finally

    close(stream)

end

=#

# stream = PortAudioStream("Microphone (BRIO 4K Stream Edit","Microsoft Sound Mapper - Output")

# Namjestite duljinu snimke (nemojte pretjerivati)

# buf = read(stream, 3s)

# Zatvorite stream

# close(stream)

# Spremite vašu snimku

# save("myvoice.ogg", buf)

glas=load("myvoice.ogg")

length(glas)

glas.samplerate

typeof(glas)

glas.data

# Napravimo mono snimku

glas_mono=similar(glas);

begin

    glas_mono.data=sum(glas.data,dims=2)

    glas_mono.samplerate=glas.samplerate

end

save("myvoice_mono.ogg", glas_mono)

glas_mono.data

glas_mono

# Pogledajmo signal

using Plots

begin

    S=glas_mono.data

    plot(S,label="Originalni signal")

end

# Vrijeme

T=range(0,3,length=length(S))

# Plot u vremenu

plot(T,S,xlabel="t (sec)",label="Originalni signal")

begin

    # Trapezna formula, približno. Računamo kosinusni i sinusni spektar

    using LinearAlgebra

    A(λ::Float64)=(cos.(λ*T)⋅S)*((T[end]-T[1])/(length(T)*π))

    B(λ::Float64)=(sin.(λ*T)⋅S)*((T[end]-T[1])/(length(T)*π))

end

# Nacrtajmo kosinusni i sinusni spektar i odlučimo koje frekvencije ćemo zadržati

plot([A B],300,5000,layout=(2,1),label=["Kosinusni spektar" "Sinusni spektar"])

begin

    # Ograničimo spektar, opet koristimo približnu formulu

    λ₀=600.0

    λ₁=4500.0

    step=0.5

    Λ=range(λ₀,λ₁,step=step)

    # Ovo traje cca 1 minutu, ali se računa samo jednom

    Aλ=A.(Λ)

    Bλ=B.(Λ)

end

# Rekonstruirajmo signal s odrezanim frekvencijama

g(x::Float64)=(Aλ⋅cos.(x*Λ)+Bλ⋅sin.(x*Λ))*step

G=g.(T)

# Usporedimo grafički

plot(T,[S G],layout=(2,1),label=["Originalni mono signal" "Odrezani mono signal"])

begin

    # Spremimo signal s odrezanim frekvencijama i poslušajmo

    glas_mono_odrezan=deepcopy(glas_mono)

    glas_mono_odrezan.data[:,1]=map(Float32,G)

    save("myvoice_odrezan.ogg", glas_mono_odrezan)

end

glas_mono_odrezan